First slide

General Planar motion

Question

A sphere is rolling down an inclined plane without slipping. The ratio of rotational kinetic energy to total kinetic energy is

Moderate

A

$\frac{5}{7}$
B

$\frac{2}{5}$
C

$\frac{2}{7}$
D

none of these

Solution

$\frac{{KE}_{rot}}{{KE}_{tot}} = \frac{\frac{1}{2} I ω^{2}}{\frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}} = \frac{\frac{2}{5} m v^{2}}{\frac{7}{5} m v^{2}} = \frac{2}{7}$

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